Xia Jiang

Chapter 4 – Learning Bayesian Networks

This chapter addresses the problem of learning the parameters from data. It also discusses score-based structure learning and constraint-based structure learning. The method for learning all parameters in a Bayesian network follows readily from the method for learning a single parameter. The chapter presents a method for learning the probability of a binomial variable and extends this method to multinomial variables. It also provides guidelines for articulating the prior beliefs concerning probabilities. The chapter illustrates the constraint-based approach by showing how to learn a directed acyclic graph (DAG) faithful to a probability distribution. Structure learning consists of learning the DAG in a Bayesian network from data. It is necessary to know which DAG satisfies the Markov condition with the probability distribution P that is generating the data. The process of learning such a DAG is called “model selection.” A DAG includes a probability distribution P if the DAG does not entail any conditional independencies that are not in P. In score-based structure learning, a score is assigned to each DAG based on the data such that in the limit. After scoring the DAGs, the score are used, possibly along with prior probabilities, to learn a DAG. The most straightforward score, the Bayesian score, is the probability of the data D given the DAG. Once a DAG is learnt from data, the parameters can be known. The result will be a Bayesian network that can be used to do inference. In the constraint-based approach, a DAG is found for which the Markov condition entails all and only those conditional independencies that are in the probability distribution P of the variables of interest. The chapter applies structure learning to inferring causal influences from data and presents learning packages. It presents examples of learning Bayesian networks and of causal learning.

Chapter 1 – Probabilistic Informatics

Informatics is the discipline that applies the methodologies of science and engineering to information. It concerns organizing data into information, acquiring knowledge from information, learning new information from existing information and knowledge, and making decisions based on the knowledge and information learned. Informatics programs ordinarily investigate subjects such as biology and medicine, whereas computer science programs do not. WordNet 2.1 defines informatics as “the science concerned with gathering, manipulating, storing, retrieving, and classifying recorded information.” The chapter also focuses on probability theory. A heuristic algorithm uses a commonsense rule to solve a problem. An abstract model is a theoretical construct that represents a physical process with a set of variables and a set of quantitative relationships among them. A model-based algorithm, therefore, makes predictions/determinations within the framework of some model. Algorithms that make predictions/determinations within the framework of probability theory are model-based algorithms. The chapter also focuses on algorithms that use Bayesian networks to reason within the framework of probability theory.

A Tutorial on Learning Causal Influence

In the 1990’s related research in artificial intelligence, cognitive science, and philosophy resulted in a method for learning causal relationships from passive data when we have data on at least four variables. We illustrate the method using a few simple examples. Then we present recent research showing that we can even learn something about causal relationships when we have data on only two variables.

Chapter 8 – Modeling Real Options

This chapter suggests that when faced with the possibility of undertaking a new project, a company must make the decision of whether to pursue that project. A standard way to do this is to perform an analysis based on the expected cash that will be realized by the project. It explains that a stock has a required rate of return (k) that is higher than the risk-free rate owing to its risk, and the expected net present value of the stock is computed using k. Similarly, a risky investment in a project has associated with it a rate, called the risky discount rate that is used to compute the net present expected value (NPEV) of the project. The determination of this expected net present value is called a discounted cash flow (DCF) analysis. A toy decision problem that contains many of the features found in actual decisions concerning real options was devised by Sercu and Uppal. The chapter presents this problem and shows how its solution can be modeled and solved using influence diagrams.

Chapter 6 – Further Techniques in Decision Analysis

This chapter presents some techniques in the use of decision analysis. Most individuals would not make a monetary decision by simply maximizing expected values if the amounts of money involved were large compared to their total wealth. When an individual maximizes expected value to reach a decision, the individual is called an expected value maximizer. In the case of decisions in which an individual would not maximize expected value, one needs to model the individuals attitude toward risk to use decision analysis to recommend a decision. One way to do this is to use a utility function, which is a function that maps dollar amounts to utilities. Risk tolerance determines the degree of risk-aversion modeled by the function. It is a property of the exponential utility function that an individuals total wealth cannot affect the decision obtained using the function. A function such as this is called a constant risk-averse utility function. If one uses such a function to model ones risk preferences, he/she must reevaluate the parameters in the function when ones wealth changes significantly. If a change in total wealth can change the decision obtained using a risk-averse utility function, then the function is called a decreasing risk-averse utility function. An example of such a function is the logarithm function.

Chapter 12 – Targeted Advertising

This chapter presents a decision theoretic approach to targeted advertising developed by Chickering and Heckerman. One way for a company to advertise its product would be to simply try to reach as many potential customers as possible. However, this could prove to be costly since there is no point in wasting an advertisement on someone who most probably will not buy the product regardless or, worse yet, who would be turned off by the advertisement. Another approach would be to try to identify those customers such that one can expect to increase the profit by sending them advertisements. It discusses that targeted advertising is the process of identifying such customers.

Chapter 5 – Decision Analysis Fundamentals

This chapter introduces decision trees that are mathematically equivalent to influence diagrams, but which have difficulty representing large instances because their size grows exponentially with the number of variables. A decision tree contains two kinds of nodes: chance nodes representing random variables and decision nodes representing decisions to be made. A decision represents a set of mutually exclusive and exhaustive actions the decision maker can take. Each action is called an alternative in the decision. There is an edge emanating from a decision node for each alternative in the decision. The expected utility (EU) of a chance node is defined to be the expected value of the utilities associated with its outcomes. The process of determining these expected utilities is called solving the decision tree. The entire process of identifying the components of a problem, structuring the problem as a decision tree (or influence diagram), solving the decision tree (or influence diagram), performing sensitivity analysis, and possibly reiterating these steps is called decision analysis. The chapter also discusses influence diagrams, whose size only grows linearly with the number of variables. The chapter also introduces dynamic Bayesian networks and influence diagrams that model relationships among random variables that change over time.

Chapter 9 – Venture Capital Decision Making

Start-up companies often do not have access to sufficient capital, but, if they could obtain that capital, they may have the potential for good long-term growth. If a company is perceived as having such potential, investors can hope to obtain above-average returns by investing in such companies. Money provided by investors to start-up firms is called venture capital (VC). It discusses that wealthy investors, investment banks, and other financial institutions typically provide venture capital funding. VC investment can be very risky. Venture capitalists are experts who analyze a firms prospects. The chapter presents a simple influence diagram based on their causal network that models the decision of whether to invest in a given firm. This simple influence diagram is for the purpose of providing an accessible introduction. It explains a detailed influence diagram obtained from their causal network.

Chapter 10 – Bankruptcy Prediction

Predicting whether a firm will go bankrupt is quite important to the firms auditors, creditors, and stockholders. However, even auditors, who should best know a firms situation, often fail to see an impending bankruptcy. Several models have been developed to predict the likelihood of bankruptcy from information about a firm. These include models based on simple univariate analysis, logistic regression, neural networks genetic programming, and Bayesian networks. The chapter provides guidance in the selection of variables and the discretization of continuous variables. The advantage of the naive Bayes model is that the number of parameters is kept to a minimum. Another possible improvement that would not increase the complexity of the network would be to use the population proportion of bankruptcies as the prior probability of bankruptcy. The chapter describes experiments testing the accuracy of the bankruptcy prediction Bayesian network. Results of these experiments are described and compared to the results obtained using other versions of the network and using logistic regression.

Chapter 7 – Investment Science

An important problem in investment science is modeling the risk of a portfolio. The chapter presents a Bayesian network for portfolio risk analysis and discusses the basics of the stock market and investing in stocks. The chapter also presents mean-variance portfolio theory, capital asset pricing model (CAPM), arbitrage pricing theory, and equity valuation models. It discusses the market equilibrium and CAPM and briefly investigates the models accuracy and industrys use of the model. Factor models try to model the relationship between expected return rates of assets and these economic variables, which are called macroeconomic risk factors. The theory does not say what the macroeconomic factors need to be. The assumptions in the factor models are also presented. The relationship between APT and CAPM is described and a commonly used factor model is discussed.